If the average of the following data is $100$ . Find the value of $p$ .

- 26

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Solution

The correct option is C $- 28$
Answer:- Given:- $¯ ¯ ¯ x = 100$
Using frequency distribution table

x f xf
10 2 20
20 4 80
30 p 30p
40 8 320
50 10 500
60 12 720
$Σ f_{i} = 36 + p$ $Σ x_{i} f_{i} = 1640 + 30 p$
Average = $\frac{Σ f x}{Σ f}$
$\Rightarrow ¯ ¯ ¯ x = \frac{1640 + 30 p}{36 + p}$
$\Rightarrow 100 = \frac{1640 + 30 p}{36 + p}$
$\Rightarrow 100 (36 + p) = 1640 + 30 p$
$\Rightarrow 3600 + 100 p = 1640 + 30 p$
$\Rightarrow 100 p - 30 p = 1640 - 3600$
$\Rightarrow 70 p = - 1960$
$\Rightarrow p = - \frac{1960}{70}$
$\Rightarrow p = - 28$
B) -28

Suggest Corrections

$23$	$24$	$25$	$26$	$27$	$23$	$24$
$25$	$28$	$24$	$29$	$19$	$20$	$x$

Daily wages	$22 - 24$	$24 - 26$	$26 - 28$	$28 - 30$	$30 - 32$
Number of workers	$23$	$120$	$100$	$110$	$105$